here, \(m\)  is the mass of the bosons, \(n=|\psi |^2\)  their number density, \(G =4\pi G_{N}m^2\)  (\(G_N\)  denotes Newton's gravitational constant), and \(g=4 \pi a\hbar ^2/m\) , with \(a\)  the \(s\) -wave scattering length Note that the
subtraction of the mean density on the right-hand side (RHS) of the Poisson
equation  can be justified either by taking into account the
cosmological expansion [1]}, [2]} or by defining a Newtonian
cosmological constant [3]}. We describe the dynamics of the pulsar's
solid crust by a single polar angle \(\theta \) , which evolves as follows:
\( I_c \frac{d^2\theta }{dt^2}&=&\frac{1}{N}\int d^3x \partial _\theta V_\theta |\psi |^2 -\alpha \frac{d\theta }{dt}; \\V_\theta ({\bf r}_p) &=& V_0 \exp (-\frac{|{\bf r}_p |-r_{\rm crust}}{\Delta r_{\rm crust}})^2 \tilde{V}(x_\theta ,y_\theta ) ;\) 
